How to set it up so it uses outside mail server

[skurudo]

You can try this article (not tested be me), it may help:

I need exim to send all outbound email through a remote mail server
http://help.directadmin.com/item.php?id=153

PS: Remember, make copy of yuor config before you change something ;)

[dezaxatul]

I'm also looking for a resolution to this?

Any help?

[skurudo]

Guys, it's many recipes how to cook a duck.
one of many - https://wiki.debian.org/GmailAndExim4

Using external smtp it's non-standart solution, it's like building a new bike.

[mehargags]

Which external Transactions mail Service are you trying to setup? there are a little different parameters for each one of them.

Currently I've successfully done it with SendGrid, MailChimp, Mandrill, Mailjet and a couple of more.
You need to set these into /etc/exim4/exim4.conf.template for the ACL, Transport & router Sections respectively.

If thats alot of work for you, I can help you with it via SSH, PM me please.